TY - JOUR

T1 - Discrete and continuous description of physical phenomena

AU - Ginzburg, I. F.

PY - 2017/7/27

Y1 - 2017/7/27

N2 - The values z of many observable quantities in the Nature are determined at some discrete set of times tn , separated by a small interval Δt (which may also represent a coordinate, etc.). Let the z value in neighbour point tn +1 = tn + Δt be expressed by the evolution equation as as z(tn +1) ≡ z(tn + Δt) = f(z(tn )). This equation gives a discrete description of phenomenon. Considering phenomena at t ≪ Δt this equation is transformed often into the differential equation allowing to determine z(t) leading to continuous description. It is usually assumed that the continuous description describes correctly the main features of a phenomenon at values t ≫ Δt. In this paper I show that the true behavior of some physical systems can differ strongly from that given by the continuous description. The observation of such effects may lead to the desire to supplement the original evolutionary model by additional mechanisms, the origin of which require special explanation. We will show that such construction may not be necessary - simple evolution model can describe properly different observable effects. This text contains no new calculations. Most of the discussed facts are well known. New is the treatment of the results.

AB - The values z of many observable quantities in the Nature are determined at some discrete set of times tn , separated by a small interval Δt (which may also represent a coordinate, etc.). Let the z value in neighbour point tn +1 = tn + Δt be expressed by the evolution equation as as z(tn +1) ≡ z(tn + Δt) = f(z(tn )). This equation gives a discrete description of phenomenon. Considering phenomena at t ≪ Δt this equation is transformed often into the differential equation allowing to determine z(t) leading to continuous description. It is usually assumed that the continuous description describes correctly the main features of a phenomenon at values t ≫ Δt. In this paper I show that the true behavior of some physical systems can differ strongly from that given by the continuous description. The observation of such effects may lead to the desire to supplement the original evolutionary model by additional mechanisms, the origin of which require special explanation. We will show that such construction may not be necessary - simple evolution model can describe properly different observable effects. This text contains no new calculations. Most of the discussed facts are well known. New is the treatment of the results.

KW - NON-LINEAR TRANSFORMATIONS

KW - SYSTEMS

UR - http://www.scopus.com/inward/record.url?scp=85028305183&partnerID=8YFLogxK

U2 - 10.1088/1742-6596/873/1/012046

DO - 10.1088/1742-6596/873/1/012046

M3 - Conference article

AN - SCOPUS:85028305183

VL - 873

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

SN - 1742-6588

IS - 1

M1 - 012046

ER -